Neuronal differentiation is characterized by changes in both the extent of intercellular coupling and the expression patterns of connexin genes that encode gap junction proteins. Using a neuroblastoma culture system, we have found that stable exogenous expression of different gap junction genes results in either retarded or accelerated response to differentiating agents. Comparing gene expression using locally produced cDNA microarrays indicates candidate genes whose expression is enhanced or depressed in the transfected neuroblastoma cells. However, the preliminary studies raise important questions regarding the technique, including threshold of detection, reliability for each of the spots in the array and detection of clusters representing gene expression patterns. The Specific Aims of this application are to apply mathematical algorithms and modify experimental techniques so as to: 1) minimize the spot ratio errors; 2) determine expected values and controllable fluctuations of gene expression; 3) build the pre-Hilbert space of standard gene expression (SSGE); 4) compute the so-called "pathologs" of gene expression for parental and transfected cells; and 5) define gene clusters within the SSGE. We expect that these studies will not only improve our use of the microarray analysis, but will develop new concepts by which such expression patterns are generally used.